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An Anatomy of Moral ResponsibilityMatthew BrahamInstitute of Philosophy, University of [email protected]

Martin van HeesFaculty of Philosophy, University of [email protected]

This paper examines the structure of moral responsibility for outcomes. A centralfeature of the analysis is a condition that we term the avoidance potential, whichgives precision to the idea that moral responsibility implies a reasonable demandthat an agent should have acted otherwise. We show how our theory can allocatemoral responsibility to individuals in complex collective action problems, an issuethat sometimes goes by the name of the problem of many hands. We also showhow it allocates moral responsibility in the classic Frankfurt example.

1. Introduction

Judgements of moral responsibility for the realization of a state ofaffairs are intimately connected to the relationship between anagents behaviour and the state of affairs involved. Roughly speaking,a theory of moral responsibility for outcomes selects a subset of agentsdeemed to be appropriate candidates for moral appraisal (blame orpraise) and/or sanctions (punishment or reward) on the basis of therebeing a significant connection between their actions and the state of

affairs in question. A great many problems fit this general descriptionof moral responsibility, in particular problems that arise when out-comes are related to a complex of agents and decisions.

Consider, for instance, what is perhaps the most widely discussedexample in the literature on moral responsibility, the so-calledFrankfurt example (Frankfurt 1969). This concerns a situation inwhich an agent performs an action but, had he not decided to performthe action, the activation of some intricate back-up mechanism (e.g.a device planted in his brain by another agent) would have resulted inhim performing the action anyhow.1 The example has, of course, been

1 See Widerker 2000 for a collection of articles dealing with various versions of the

example.

Mind, Vol. 121 . 483 . July 2012 Braham and van Hees 2012

doi:10.1093/mind/fzs081 Advance Access publication 4 December 2012

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used to call into question the assumption that the existence of alter-

native possibilities is a necessary condition for ascribing moral re-sponsibility. Though the example is usually discussed in terms of

responsibility for actions, it also applies to responsibility for outcomes.That is, the example also calls into question whether agents are re-

sponsible for the outcomes of their action if the outcomes would haveoccurred anyhow. Also relevant for us here is that the outcome de-pends on what other agents do. That is, the setting is an interactiveone the outcomes of at least some possible decisions cruciallydepend on the actions of others (here the triggering of the back-upmechanism).

Although the Frankfurt example incorporates this interdependencybetween some of the actions of the individuals, since the back-upmechanism is not triggered it is in the end only the action of one ofthe two individuals that actually effects the outcome. In contrast, thereare many real-life situations in which the actions of many different

agents do in fact contribute to a particular outcome. In these casesascertaining who is to be held responsible for the resulting outcome isknown as the problem of many hands (Thompson 1980), a promin-ent class of which is covered by the so-called Tragedy of the Commons

(Hardin 1968).2

A further class of significant cases concern decision-making in com-mittees. In a recent and important paper, Pettit (2007) has argued thatcircumstances in committee voting exist the so-called DiscursiveDilemma in which none of the constituent members of the com-mittee can be said to be morally responsible for the outcome of a vote.

He christens this the problem of no hands. Pettit considers suchcircumstances to be particularly onerous because if such responsibil-

ity voids exist, then committee members have an incentive to organ-ize their activities in a self-serving way while at the same time beingable to avoid any responsibility in the event that a harm occurs

(Pettit 2007, p. 197). As a way around this problem Pettit invokesthe concept of collective responsibility. But this carries with itthorny metaphysical and normative implications, yielding the ques-

tion whether it is indeed impossible to establish individual responsi-bility in the circumstances he describes.

The objective of this paper is ambitious. We do no less than providea general analysis of the necessary and sufficient conditions for

2 See Bovens 1998 and Ostrom 1990 for collections of real-world cases of the Tragedy of the

Commons.


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assigning moral responsibility to individuals that can systematicallycover the problems of the type that we have just listed. To do so, wewill introduce a simple methodological innovation: we take the cases

of interactive decision-making as the general case and our startingpoint. For our analysis of these cases we adopt a framework that isnatural to such circumstances, that of game theory. The advantage ofdoing so is three-fold. Firstly, the results apply to simple and complexdecision situations alike because simple decision situations are specialcases of the general model. Secondly, it allows us to adumbrate a set ofconditions that more or less define an algorithm for cutting throughthe thicket of concepts and examples that characterize the analysis

of moral responsibility in general and cases of joint actions inparticular. Thirdly and we believe most significantly it abstractlydescribes the different ingredients of our theory of responsibility. It isfor this reason that we say that we present an anatomy of moralresponsibility.

Before beginning we should briefly mention how our analysis isrelated to the existing literature. A first connection is that a centralfeature of our anatomy is what we denote the avoidance potential.This is a formalization of the idea that was independently put

forward by McKenna (1997), Wyma (1997), Otsuka (1998), andHetherington (2003), in the context of the debate about Frankfurt-style examples. It states that moral responsibility requires that theperson in question could escape being blamed or punished for par-ticular outcomes by avoiding being an author of the outcome.Another connection is to the important recent contribution byVallentyne (2008). Like ourselves, Vallentyne develops a formalframework for analyzing outcome responsibility. However, whereas

we follow Vallentyne in emphasizing the importance of there beinga causal link between the agents actions and the outcomes for whichhe is to be held responsible, our rendition of these causal relationsdiffers substantially from his. One reason is that our informationalframework is richer: we assume information is given about the inter-active setting in which individuals make their decisions, and thenderive attributions of causality from it. Vallentyne abstracts fromthe background in which the decisions are made and describescausal relations purely in terms of exogenously given objective

probabilities.As a guide: we start (in Sect. 2) by demarcating our concept of

moral responsibility. We define it in terms of three conditions theAgency Condition, the Causal Relevancy Condition, and the


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Avoidance Opportunity Condition. Whereas much of the responsibil-ity literature focuses on the kind of agency that is needed for respon-sibility, we ignore this issue altogether and simply assume that the

Agency Condition is always fulfilled. This allows us to focus onwhere the contribution and innovation of this paper lies: the analysisof the Causal Relevancy Condition and the Avoidance OpportunityCondition.

In section 3 we introduce and expound upon some basic game-theoretic concepts that we will use. Drawing on our recent work(Braham and van Hees 2009), we introduce and summarize the con-ception of causal contribution that constitutes the first central com-

ponent of our analysis in section 4. In section 5 we operationalize oursecond key component of moral responsibility: the avoidance potential;and in section 6 we complete our anatomy in full. In section 7 weapply our formal theory to the analysis of the three puzzles that welisted right at the start. For the Frankfurt case, we show that ouranalysis supports the conclusion that a person can be morally respon-sible for the realization of a state of affairs, even if there was no courseof action available to him that would have led to a different outcome.Although this conclusion is nothing new, the justification is novel: on

our account the important consideration is not whether a personcould have realized a different outcome but whether he could haveavoided making a causal contribution to it. For the Tragedy of theCommons and the Discursive Dilemma we lay bear the conditionsthat have to be met in order to allocate responsibility to the individualactors. We close with some concluding remarks in section 8.

2. Moral responsibilityThe concept and cognates of moral responsibility are richly ambigu-ous and there exists no standard terminology. Our first task is todelineate the conception of moral responsibility for which we willprovide a formal framework and to bracket out certain issues.

First, the variety of outcome moral responsibility that is at issue inthis analysis is retrospective: it is the moral responsibility that an in-dividual bears towards some realized outcome or state of affairs.3 It isabout what has happened, such as Jones being killed, the pastureover-grazed, or a particular policy being approved by a committee.Retrospective moral responsibility can be said to come in different

3 The distinction between an outcome and a state of affairs will be clarified in Sect. 3.





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forms. Our conception of moral responsibility is closely related to thenotions of blameworthiness and praiseworthiness: we say that a personis morally responsible for a bad (good) outcome if it is appropriate or

justified to blame (praise) the person for the realization of theoutcome.4

To pin-point our conception of moral responsibility among thevarious usages of this term we need to set it off from three conceptionsthat have dominated recent discussions: attributive responsibility ,accountability , and substantive responsibility. Watson (2004), forinstance, speaks of attributive responsibility when an outcome bearsthe authorship, hallmark, or stamp of the person. This is weaker

than our notion, given, as Watson argues, that it does not involve theavailability of alternative courses of action (our third condition). Incontrast, Watson uses accountability to refer to judgements that doin fact presuppose such availability, and in this sense it could be saidthat this notion bears close resemblance to our conception of respon-sibility as blame- and praiseworthiness. In contrast, Scanlon (1998)uses attributive responsibility in a way that is similar to Watsonsaccountability and hence that conception can be said to resembleours. Indeed, Scanlon does not set off attributive responsibility from

accountability but rather from substantive responsibility, which isabout the duties we have towards each other and which thus is, at leastpartly, a notion of prospective responsibility.

Our conception of moral responsibility as blame- and praiseworthi-ness is to be characterized by three conditions, the first two of whichare:

Agency Condition (AC) The person is an autonomous agentwho performed his or her action

intentionally

Causal RelevancyCondition (CRC)

There should be a causal relation be-tween the action of the agent and theresultant state of affairs

Although there are many different ways of filling in these conditions,on most plausible renditions of moral responsibility both of these

conditions are necessary. Firstly, assuming autonomy includes4 We say that it is closely related to, rather than equated with, these concepts because we

do not want to preclude the possibility of being morally responsible for neutral outcomes

(outcomes that are neither bad nor good).





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normative competence, (AC) captures that we do not blame or praiseagents who cannot make normative assessments. Furthermore, (AC) isnecessary because we may do many things that effect outcomes but do

not bear the mark of authorship, where such authorship is a require-ment for blame or praise to be justified or appropriate your slippingon the ice that knocks someone over is a cause of their broken arm,but their broken arm does not bear the hallmark of your goals andhence we will not blame you for it. Note that the kind of intentionalitythat (AC) requires is not examined here. As explained below, wesimply assume the condition is always satisfied and focus on theother conditions for moral responsibility.

(CRC) is necessary because we cannot say that an outcome bearsthe stamp of authorship of a person if the person played no causalrole in bringing it about (the outcome may correspond to their goalsand norms but that does not mean they authored it) the childshooting his cap gun did not bring the plane down and we will there-fore not blame him for the crash.

Whereas the two conditions are necessary, they are not yet sufficientfor a judgement about a persons praise- or blameworthiness.Consider the bank clerk who hands over the money to a bank

robber who threatens to take her life and suppose that (AC) and(CRC) are satisfied. Even though the two conditions are fulfilled, wewill not usually say that the clerk can be blamed for handing over themoney, let alone that one may impose further censure and sanctionsfor not having complied with the demands. The question is, then,what additional necessary condition is needed? A common line ofthought is that some form of control other than being a causalfactor is required. In Watsons (2004, p. 280) view, because blaming

responses potentially affect the interests of those blamed, moralresponsibility is closely related to the issue of avoidability. Wepostulate:

Avoidance Opportunity Condition (AOC):The agent should have had a reasonable opportunity to have doneotherwise

The question, now, is how this avoidability is to be understood. Notethat we do not say that the agent should have had a reasonable op-

portunity to realize an alternative outcome; the condition is formu-lated in terms of alternative actions rather than outcomes. We oftenhold individuals responsible for some outcome even though theycould not, on their own, have prevented it from occurring. The





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rationale for this can be highlighted by two very simple examplesinvolving causal overdetermination.

Consider, first, the canonical example of Two Assassins. Two assas-

sins, in place as snipers, shoot and kill Victim, with each of the bulletsfatally piercing Victims heart at exactly the same moment. Clearlyneither assassin could have changed the outcome (Victim dies) bynot shooting. Yet we do not want to say that they are, as a result,not responsible for Victims death. For the second example, consider acommittee that makes its decision on the basis of the majority rule. Ifthe members voted unanimously in favour of some proposal, thenclearly none of the individuals could have changed the outcome by

voting differently. As in Two Assassins, we do not want to say that thecommittee members are not responsible for the decision to pass theproposal. Hence, being able to unilaterally control outcomes is toostrong a condition.

Our account of the required avoidance opportunity is motivated bythe views developed independently byMcKenna (1997), Wyma (1997),Otsuka (1998), and Hetherington (2003). Ignoring the details of theiraccounts and stating it in the terminology we use here, their views canbe summarized by the principle that one can only be morally responsible

if one had reasonable opportunity not to be so. The nub of the idea isthat a person is an apposite target of censure and sanction for somestate of affairs only if, to paraphrase McKenna (1997), it was withinher power to reasonably choose notto be an author (or co-author inthe presence of multiple causal conditions) of that state of affairs. Inthe bank robber example, we do not submit the bank clerk to, say,censure and sanction for co-authoring the state of affairs in which thebank robber walks out with the loot: she did not have a reasonable

opportunity not to be such a co-author.The conditions for responsibility that we have laid out here allow usto give further precision to this principle. A person is not responsibleif (AC) or (CRC) is not met. An important caveat is that we willassume but without any justification that under the full informa-tion setting we presuppose (see below) an autonomous agents deci-sion to act non-autonomously never undermines the agentsresponsibility for the consequences of the non-autonomously per-formed actions. Simply put, if we know the consequences of excessive

drinking, then, if we deliberately become drunk, our drunkenness doesnot undermine our responsibility for those consequences. (AC) is stillsatisfied and the required avoidability therefore comes down to havingthe possibility to avoid meeting (CRC): it consists of the possibility to





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break the causal link between the agent and the outcome. To illustrate,in Two Assassins, by not shooting, an assassin would not have pre-vented the outcome, but would have ensured that he would not be

causally effective for it (we will return to this example in Sect. 4).Similarly, for the committee example, by voting against the proposalan individual committee member would not have prevented the out-come, but would have ensured that he would not be causally effectivefor it being approved.

Given that our subject is moral responsibility, the alternative op-portunity should also be a reasonable one. Whether that is indeed so isa normative issue and can only be established by reference to a set of

norms and values. Our analysis is general enough to be compatiblewith different normative views. We assume, however, that within thecommunities to which our anatomy of moral responsibility applies,there is consensus about the reasonableness or unreasonableness or, aswe shall prefer to call it, the eligibility or ineligibility of the variouscourses of action that are open to the agents.

Before proceeding, we recognize that all three of these conditionscarry with them their own special problems. For the purposes of thisanalysis we will simply assume that (AC) is always satisfied; that is, the

relevant actions are performed intentionally and the individuals in ouranalysis are assumed to have a capacity to reflect on their beliefs anddesires and exercise some form of control over what they do, or refrainfrom doing: they are normatively competent in the sense required tospeak about autonomous agents. Ignoring how (AC) is to be filled outin detail allows us to concentrate on fleshing out and giving formaland abstract structure to the second and third conditions. It is herewhere the innovations lie. Another important limitation of the ana-

lysis concerns epistemic considerations. If an agent knew, could haveknown, or should have known, that a certain action of hers could leadto a particular outcome, then we shall assess her responsibility for theoutcome differently than if she could not possibly have known, orneed not have known, that the outcome would have resulted. Weignore these issues in this paper by restricting ourselves to situationsin which individuals have complete information. That is, they know theactions and omissions available to them and to others, and also knowwhich outcomes follow from which particular combinations of ac-

tions. The only information they may not have pertains to what theother agents will do; since the consequences of an agents actions oftendepend in part on those other actions, the individuals may thus beignorant about the exact consequences of their actions.





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3. The formal framework

The elementary concept that we need throughout is that of a game.

Very generally, a game specifies who can do what, when, and to whateffect, as well as the individuals preferences regarding the variousoutcomes. We use the information provided by a game as the basis

of responsibility assignments. Formally, a game G is an n+ 4-tupleN, X, S1, , Sn,p, R

n, where (1) N (with cardinality n) is a finite

set of agents (players); (2) X a finite set of outcomes; (3) for eachi 2 N, Si is a finite set of possible strategies; (4) p is an outcome func-

tionfrom the set of all strategy combinations i2NSi, or plays, onto X

(p being onto Xmeans each element ofXis an outcome in at least one

play, with a play being denoted by a strategy profile sN s1, , sn;and (5) Rn is a preference profile, that is, an n-tuple of preference

orderings (one for each individual) over X.The elements of the set X are taken to be possible worlds and are

called outcomes. The (non-empty) subsets A X are called states of affairsand describe one or more aspects of an outcome. Thus, whereasx may, for instance, be the outcome in which Bob is elected to be thenew leader of the labour union, A may represent the state of affairs in

which a male person is elected to be the new leader and B the set ofoutcomes in which no new leader is chosen, etc.5 The distinctionbetween states of affairs and outcomes is important. A person may

be responsible for an outcome without being so for all of its aspects(I may be responsible for Bob being elected but I need not be so for

the fact that a man is elected, as there may have been no female

candidates on the ballot); conversely, one may be responsible for a

state of affairs without being so for the outcome (I may be responsiblefor the election of a male candidate perhaps because I vetoed all

female candidates without being so for Bobs election).A strategy is a course of action available to the agent. Generally

speaking a strategy is a bundle or complex of actions. For instance,the strategy shoot consists of all those physical events that result in a

shooting, such as picking up a gun, aiming, curling a finger around

the trigger, etc. In general terms it is a plan of action or a protocol ofwhen to do what. A game also treats omissions as strategies. A strat-

egy of not shooting, for instance, is any set of actions that does not

5 Note that we have x 2 A and A \ B 1: To avoid cumbersome notation, we shall drop

the set brackets when a state of affairs describes all aspects of an outcome, i.e. when it is a

singleton set. In such cases we denote both the outcome and the state of affairs simply by x

rather than by x and {x}, respectively.





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contain certain actions that are necessary for shooting. To borrow

Lewiss (2004) pithy description, omissions are not absences that

cannot be considered causal relata by reason of their nonexistence.

Finally, the outcome functionp assigns a particular outcome to eachcombination of strategies. The function is completely abstract: it may

be determined by empirically ascertainable laws of nature, such as the

strength required, say, to lift a fallen tree that has trapped a person; orit may be a matter of social law and convention, such as a decision rule

that determines who has the authority to do certain things. In any caseit is a statement of certain regularities, generated either naturally or

conventionally . Note that it being a function does preclude the pos-

sibility of there being indeterminacies.In itself, a specification of the players, their strategies, the outcomes,

and the outcome function does not give us information about what

the agents will do. For that purpose game theorists also specify the

preferences of the individuals and use a solution concept. The existence

of a preference profile expresses the assumption that agents are able togive a consistent ordering of their wants, desires, needs, and interests.Given a conception of rationality, a solution concept specifies how a

game will be played: it consists of a subset of plays. For our purposes it

is important not only to know what the agents will do given a game

and an assumption about individual rationality, but also what wouldhappen if a player were to adopt a strategy that may not be rational.

For this reason, we assume that for each player i and each strategy siavailable to her, we can assign a probability distribution over the plays

in which iperforms si. We assume these probabilities describe justified

expectations about the possible actions of the others. For the purposesof this paper we will not dwell on the precise nature of these prob-

ability distributions, or how they are related to a solution concept.6

Before we proceed, it is important to point out that the specification

of the relevant game is not an innocuous choice. To see this, considerBeebees (2004) Queen of England Problem. Suppose Bob promised

to water Joans plant but for some reason failed to do so with the

consequence that the plant died. To model this situation it is reason-able to focus on a game in which Bob and Joan are the only players.

Now suppose we derive the judgement that Bob caused the plants

death. It may well be the case that on the theory of causation yielding6 Note that the probability distributions are defined for any si, hence also for those that

have a zero probability of being adopted by i. See Brandenburger 2007 for a discussion of the

use of such probability functions in a game-theoretic framework.





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that judgement we would also have to infer that the Queen of

Englands failure to water the plant is a cause of the plants death:

the reasoning that led to the judgement that Bobs omission is a causal

factor may also apply to the Queens omission.7 However, the Queenis not assumed to be part of the game and thus the way a game isdefined already selects the relevant individuals whose behaviour is to

be appraised.In the context of Mackies (1965; 1974) theory of causation, which

we broadly adopt, the ingredients of the analysis are what he calls thecausal field.8 This notion presupposes knowledge of which part of the

causal chain that led to some action is relevant for the assessment of a

persons causal contribution and which part is not. In the Queen ofEngland Problem, Bobs action is taken to be part of the causal fieldwhereas the Queens omission is not. Given that we are developing anaccount of moral responsibility, we could say that the game not only

specifies the causal field but also the moral field; the game contains

all of the normatively relevant information.To give another example of the relevance of the choice of which

game we take to analyse responsibility, suppose we want to determine

which members of a voting committee are responsible for a decision

they made. If we restrict our attention only to the actual decision, then

the game will only describe the situation at the time of the actual vote:the given set of players, the voting rule, the various outcomes to which

the different combinations of votes would have led, and the actualoutcome. Given this restricted information, we may come to the con-

clusion that some member of the committee can be exonerated be-

cause, say, she voted against the eventual outcome. However, if weextend the game by incorporating information about, for instance,

how the committee came into being in the first place, that committeemember may well be responsible after all perhaps because if she had

not agreed to join the committee the vote may not have been taken atall. In the following analysis we will indeed focus only on the givengameat hand, which means we will not handle moral responsibility for

past choices.

7 On the account of causation that we present in the next section this is indeed the case.

After all, had Bob watered the plant it would have lived; and had the Queen of Englandwatered the plant it would have lived. On this problem see also McGrath 2005; Sartorio 2007.

8 Mackie actually draws on Hart and Honores (1959) seminal analysis of causation in the

law. They say that a causal ascription picks out unusual behaviour among prior contextual

considerations.





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Taking some specific game as the starting point of the analysis, thatis, presupposing a moral field, does not make the analysis arbitrary.First of all, we are often interested in assigning responsibility in well-

defined and specific contexts, such as when we want to know who isresponsible for a specific committee decision, in so far as that respon-sibility can be traced back to the decision-making process within thecommittee. In these cases, the research question at least in part deter-mines the moral field. Secondly, the relevance of the moral field in-dicates that assignments of moral responsibility are partly determinedby our prior moral expectations: there is, we assume, no normativelyneutral way of arriving at such judgements. This means that the choice

of the game should be carefully justified; it does not mean that suchjustification is impossible.9

4. Making a causal contribution

In order to ascribe moral responsibility for some state of affairs to anindividual we must precisely parse her causal connection to that stateof affairs. This is the condition (CRC) stated in section 2. Two re-

marks are necessary before we begin. First, although we use the termcausation or causal efficacy, we are aware that on occasion it wouldbe more precise to use the expressions contributory effect, conven-tional causality , or conventional generation, because the term caus-ality generally refers to the connection between two events that arerelated by some regularity or law of nature. The cases that we focuson are governed by legal norms and social conventions and not merelyby laws of nature as such. For instance, that a house burns downfollowing the outbreak of a fire of a certain size and intensity follows

from the regularities that we call laws of nature; that a particularpolicy is implemented following the agreement of a given set of peoplefollows from legal rules and conventions. That is, the states of affairs inour examples may not be nomically related to their causes.10 Toadopt this other terminology would, however, burden the discussionwithout adding anything. In fact, we need not do so since we areprimarily concerned with causation for particular or singular events

9 The problems here are inherent to any description. See Sen 1980 for an insightful

analysis.

10 This distinction is discussed in more detail in Kramer 2003, p. 280.





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(or causes in fact, in legal terminology).11 The conception of a causethat we adopt, but do not defend, is that of difference-making. InLewiss (1973, p. 557) paraphrase of Hume: We think of a cause as

something that makes a difference, and the difference it makes mustbe a difference from what would have been.

We assume, as is general in legal theory (especially in tort law), thata cause is a relation of dependency to be understood in terms ofnecessary or sufficient conditions (Honore 1995). In particular, weassume that it is a form of dependence that subordinates a criterionof necessity to that of sufficiency and replaces the idea of identifyingsome event as the cause with that of a causally relevant factor. This

conception ascribes C causal status for E if it satisfies the followingcriterion, known as the NESS test (Wright 1988, p. 1020):

Definition 1:C is a (NESS-)cause of E if, and only if, there is a set of sufficientconditions for E such that: (1) C is a member of the set; (2) allelements of the set obtain; (3) C is necessary for the sufficiency ofthe set.12

In words: C is a causal condition for E if C is a necessaryelement of a

sufficient set of conditions for E (NESS). Or, somewhat more pre-cisely, C is part of a set of conditions that are together sufficient for Eand is necessary for that set of conditions to be sufficient for E. In the

11 For the reader unfamiliar with the literature on causation, the term singular causation

comes from the singulargeneral distinction of types of expressions. For propositions about

causation, we say that Macks drinking of a gallon of wine was a cause of his drunkenness is a

statement of singular causation. In contrast, drinking a gallon of wine causes drunkenness is ageneral statement and implies a covering law.

12 The NESS test was first stated in Hart and Honore 1959 and can be traced back to J. S.

Mill. The NESS test was also formulated by Mackie (1965, 1974), in terms of INUS conditions:

an insufficient but necessary part of a condition which is itself unnecessary but sufficient for

the result. Note that Mackies (1965) original formulation was more restrictive than the NESS

test as discussed in Wright 1988 because it contained a condition that ruled out causal over-

determination (condition 4), which he later dropped (Mackie 1974). For a critique of the NESS

test as an account of causality, see Cane 2002. Halpern and Pearl 2005 provides a fully fledged,

formal structure of the NESS test that takes into account some of the problems that the NESS

test faces. We do not need the apparatus here, however. As a point of contrast, in his formal

framework Vallentyne (2008, p. 63) makes use of an entirely different conception of a cause.He assumes that the relevant causal connection is that the choice increases the objective

chance that the outcome will occur, where objective chances are understood as objective

probabilities in the sense of single case propensities. We discuss reasons for not adopting

this model in Braham and van Hees 2009.





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case in which all elements of the set are necessary for the sufficiency ofthe set, we call such a set a minimal sufficient condition for E.13

For our purposes it is helpful to note here that the NESS test readily

accounts for cases of causal overdetermination. The reason for this isthat an event is attributed causal status even if, due to the presence ofother actually or hypothetically sufficient sets, it was not necessary forthe result in the relevant circumstances. To see how this works, recallthe case of Two Assassins (Sect. 2). There are two sets of minimallysufficient conditions for Victims death that were present on the oc-casion, namely, each assassins shot. Thus, each assassin contributed acausal factor for Victims death. Consider another case: Three

Walkers. Suppose three individuals are walking in the woods andthey come across an injured jogger trapped under a fallen treetrunk. It takes at least two to lift the trunk and rescue the joggerbut as it happens all three do the lifting. Here there are three possiblesets of actions that are minimally sufficient for the rescue and eachrescuer has performed an action that belongs to at least one (in facttwo) of these. Thus, each of the rescuers actions can be attributedcausal status.14

To formulate this notion of causality in game-theoretic terms we

introduce some additional notation. First, for all T N, we call anelement sT ofPi2TSi a T-event: it describes the event of the membersofTperforming the actions described by sT (ifT 1 we may call sTa non-event); we shall write si or sT instead of sNfig or sNT,respectively. Given an event sT, si denotes the strategy of i 2 T, forevent s0T, s

0i is the element played by i 2 T in s

0T, etc. Furthermore,

we write sT, sT to denote the play of G that consists of the com-bination of the (mutually exclusive) events sT and sT. We let psT

denote the set of outcomes that can result from the event sT.

15

Notethat s1 X.

Definition 2:A T-event sT is a sufficient condition for A X if and only ifpsT A

13 Sometimes the NESS test is restricted by imposing the additional requirement that the

sufficient sets must always be minimally sufficient (see Mackie 1965, 1974; Wright 1988; and

Halpern and Pearl 2005). We do not use this strengthened version, however, because it suffersfrom a number of paradoxical problems, which are discussed in Braham and van Hees 2009.

14 More examples are discussed in Braham and van Hees 2009.

15 Formally, psT fpsT, sTjsT 2 i62TSig:





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For any sU and sT, call sU a subevent of sT if U T and if eachmember of U adopts the same strategy in sU as in sT. The game-theoretic rendition of the NESS test becomes:

Definition 3:Given a play sN, individual i makes a causal contribution to A (heractions were a causal factor) if, and only if, there is a subplay sT ofsN such that

(1) sT is a sufficient condition for A

(2) the subevent sTfig is not a sufficient condition for A

Note that the second clause entails that the individual had analternative strategy which could have led to a different outcome. IfsTfig is not sufficient for A, then by definition there is a strategys

0i for

iand a combination of strategies s0T for the players outside ofTsuchthat ps0i, sTfig, s

0T 62 A. Thus, according to our account, being a

causal factor entails the availability of an alternative course of actionswhich might have avoided the realization of the state of affairs.However, as we shall see in the next section, this kind of alternativepossibility alone is inappropriate for constituting moral responsibility.

Before proceeding we need to acknowledge a limitation that arisesfrom our focus on games in normal form. In such games, the NESStest has problems dealing with some types of strategies, namely, thosecomprising conditional actions. Suppose Bob adopts the strategy ofpainting his garage door if, and only if, his son does not do so. If wewere to model the situation as a normal form game, Bobs strategywould be said to be a NESS condition for having the door painted: anyoutcome resulting from it would lead, by assumption, to the doorbeing painted. Bob would thus be said to have made a causal contri-bution to the outcome even when it turns out that he was reading thenewspaper as his son painted the door. For cases in which such con-ditional strategies exist, we should apply the NESS test to the under-lying games in extensive form, rather than to the game in normalform. We do not go into this issue here and except for our discussionin section 7.3 we assume strategies comprise non-conditional actionsonly.

5. Having a reasonable opportunity to do otherwise

Like the Causal Relevancy Condition (CRC), the AvoidanceOpportunity Condition (AOC) requires filling out. As we said, we





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take it as given that for a person to be a legitimate target of moralcensure and sanction they must have had a reasonable opportunity tohave avoided (co-)authorship of the outcome, and this opportunity

must be reasonable by some criteria.Similar to our handling of (CRC), we proceed abstractly. We take a

mere opportunity to be a strategy simpliciter, and a reasonableoppor-tunity to be a strategy of a particular kind, which, in our view, has twoproperties. The first property refers to the possible consequences ofadopting that strategy. Since those consequences are at least partlyaffected by what the others do, we should take account of these stra-tegic interdependencies. For this purpose we introduce the notion of a

strategys avoidance potential, which is the potential for avoidingauthorship. The second property is that the strategy is eligible bysome standard.

To define this first property, the avoidance potential, we assume theexistence of a family of subjective probability distributions describingthe justified beliefs (as mentioned in Sect. 3). Using our formal ap-paratus, we say that for any game G and any i, psijsi is the prob-ability of the others playing si if i were to adopt si. Furthermore, welet hA, si denote the set of strategy combinations si of the otherssuch that si is not causally effective for the realization of A in the playsi, si. We now have:

Definition 4:The avoidance potential, isi, A, of a strategy si 2 Si for a state ofaffairs A, equalsX

si2hA, si

psijsi

The avoidance potential should not be confused with the idea ofcontrol over outcomes (such as in van Inwagens (1978) Principle ofPossible Prevention). What is crucial to the strategys avoidance po-tential is that we do not examine whether it may yield a state of affairsdifferent from A but, as we have said earlier, whether the strategy failsto be a causal factor (by the NESS test) in the realization of A. Thisdistinction is important because our definition of avoidance potentialmerely cuts the causal connection between the strategy and the out-come, while the stronger condition of control would establish a

causal link to an alternative outcome.To get to grips with the avoidance potential, consider once more the

case of Two Assassins. It now is easy to see why both Assassins areindeed responsible for Victims death. Consider Assassin 1. We know





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from section 4 that just like Assassin 2, he is causally effective for it by

way of the NESS test. The crucial point is that he could have avoidedbeing a causal factor for the realization of Victims death: if he had not

shot, he would not have been causally effective. Hence, assuming that(AC) is satisfied, he is responsible even though he could not haveprevented Victims death. The same argument applies in toto toAssassin 2.16

As such, the avoidance potential is still too raw and this brings us tothe second property. A strategy may increase the probability of avoid-ing a particular outcome but it may not be eligible in the sense that

there are reasons why it should not be performed. To fix ideas about

this requirement recall the example of the bank clerk (Sect. 2). Eventhough the avoidance potential for not handing over the money (sup-

pose she could press an emergency button and lock the doors) is lowerthan handing over the money, we do not want to hold the bank clerkresponsible for the bank robbery given that her life was at risk, it

would not have been appropriate to demand that she refuse to complywith the demands of the robber. Similarly, and less grimly, we want to

be able to distinguish between criticizing someone causing pollutionby taking Sunday pleasure drives dont be a spoilsport, Im havingsuch fun and someone causing the same amount of pollution by

driving someone to a hospital dont be ridiculous, my wife was inlabour.

The avoidance potential thus needs to be refined in a specific way.The alternative strategies that make up the potential should be eli-

gible or acceptable according to some standard. We use the termeligibility, which we take from the freedom literature. This notion,which was introduced by Benn and Weinstein (1971) and later dis-

cussed by Day (1977), Jones and Sugden (1982), and Sugden (1998), isthat when we evaluate a persons freedom to do something we gen-erally have to make some restrictions about what these things or

doings are. Assuming, for our purposes, a conception of freedomin which freedom consists of the possibility that an agent performssome action or actions of various kinds, we may be faced with all sorts

of possibilities. There are opportunities, however, that do not appearrelevant to the assessment of our freedom. Cutting off our ears is an

16 As a point of comparison, Vallentyne (2008) views neither of the two assassins respon-

sible for Victims death since the outcome occurs no matter what the other does. Vallentyne,

however, does ascribe responsibility to each assassin for the act of shooting.





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example. In Benn and Weinsteins (1971, p. 195) opinion, the reason is

that this is not the sort of thing anyone, in a standard range of con-

ditions, would reasonably do, i.e., no one in his senses would think of

doing such a thing (even though some people have, in fact, done it).The nub of the matter is that, on this view, the presence of an

ineligible opportunity to do something cannot be said to be a relevant

freedom affecting our responsibility.17 The underlying intuition is thatin the same way as an ineligible opportunity should not be considered

to have a substantial effect on our freedom, the availability of such astrategy should not be considered to affect our responsibility. In other

words, a person is to be excused for the realization of some bad out-

come, or does not deserve praise for a good one, if its avoidance wasonly feasible by the adoption of an ineligible strategy.

Obviously the question is what constitutes an eligible strategy. For

now we shall simply presuppose the existence of some theory about

what an eligible strategy means and give the conception formal con-

tent as follows:18 for each individual i, eligibility is represented by amapping Ei that assigns to each contingency si a subset of the indi-viduals strategies which, given those other actions, are eligible. Note

that eligibility is taken to be a context-dependent notion. If the N i

players, for instance, perform actions that would result in serious

wrongdoing unless itells a lie, then the act of lying may well be eligibleeven though in other circumstances (such as if the actions of other

agents could not result in wrongdoing) it may not be. As we arenot interested here in fleshing out a normative theory (the substance

of eligible alternatives), but only in investigating structural

17 This does not deny that it is in fact a freedom in the sense of purely unconstrained

opportunity and that it may be valuable to have such freedoms. For this, see Carter 1999.18 Eligibility could be welfaristic in the sense that strategies should be welfare maximizing

by some measure; or they could be deontic in the sense that they do not violate basic obli-

gations. For our purposes we need not commit ourselves to any particular position. It is

important to note that different positions may yield different responsibility judgements.

Consider the following possible objection raised by a referee. A can avoid doing a small

amount of damage to Bs car, which has stalled on the road, only by doing a significantly

larger amount of damage to hers by swerving into a ditch. Even though A had no reasonable

opportunity to do otherwise, some may still believe she is responsible for the damage done to

Bs car. On our view, rather than forming a counterexample, the example hints at the possi-

bility of conflicting views on the proper normative basis of our eligibility judgements. On a

purely consequentialist account of eligibility, As driving into Bs car may be acceptable andtherefore she is not responsible for the damage she inflicted. On the other hand, under an

extreme deontological view A could be morally responsible because she has a moral obligation

never to harm others, an obligation which holds also when the harm avoids greater harm to

ones own property.





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features the anatomy of a particular form of moral responsibilityin games, we refrain from any further exploration of the nature ofthese eligibility functions.19

6. Formal conditions for moral responsibility

We have now reached the stage where it is possible to give a crispaccount of our method for assigning moral responsibility. It consistsof three formal conditions that together are necessary and sufficientfor selecting the set of individuals who are legitimate objects of moralcensure and sanction. Call a responsibility game a triple G,G, E,

where Gis a game, G the family of probability functions (one for eachstrategy of each individual) associated with a particular solution con-cept and reflecting the justified beliefs of the agents, and E a set ofindividual eligibility functions (one for each individual).

Definition 5:In a playsi, si of a responsibility game G,G, E an individual i ismorally responsible for a state of affairs A if and only if:

(1) For all i 2 N, i is an autonomous agent and acts in-

tentionally in the relevant sense (i.e. (AC) is satisfied)

(2) si was a causal factor for the realization of A

(3) i has some eligible s0i for which the avoidance potentialfor A is greater than that of si, i.e. for somes0i 2 Eisi, is

0i, A > isi, A

The definition is general in that it accounts for the ascription ofmoral responsibility in one- or n-player normal form games of com-

plete information. Except for the conditional strategies discussed insection 4, the analysis is suitable for a very broad class of interactivedecision-making.

The definition is a result in itself because it provides a clear set ofvariables and a relation between these variables for discussing moralresponsibility. That is, the definition informs us about the data andbase-relations that need to be accounted before we can legitimatelypass judgement on a persons behaviour with respect to some out-

come. Many of the classic examples that are discussed in the modernliterature on moral responsibility do not actually take account of the

19 See van Hees 2010 for a recent analysis of such functions in the context of assessing the

value of our freedom of choice.





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full range of variables that we have introduced in our definition. So,for instance, none of the examples that are discussed in either Fischerand Ravizza 1998 or Sartorio 2007 mention preferences and solution

concepts; and while these are mentioned in Johnson 2003 andSen 1974, these discussions are basically restricted to eligibility consid-erations. Similarly, while Goldmans (1999) responsibility-based solu-tion to the paradox of voting (it is not rational to do so) is close toour definition because it is based on the NESS test, it does not take thebelief structures (the probability distributions) that are an integral partof the avoidance potential into account.20 In our approach all thesevariables are considered (e.g. preferences enter the equation via the

avoidance potential). It is also worth noting that the definition is silentabout socially optimal states of affairs. No burden is placed on a playerto necessarily choose the socially optimal outcome (by some standard)and thus hold the player responsible for its non-occurrence if they

happen to have chosen a strategy leading to a sub-optimal outcome.To avoid any misunderstanding, although the second clause con-

tains a quantifier we do not impute amounts of responsibility to theplayers. We have not taken a stand on whether moral responsibilitycan be quantified or distributed in some particular way, and nor willwe do so here. At best we can say that, when the conditions are ful-filled, an agent is said to bear someresponsibility for the realization ofthe state of affairs in question.21 Quantification is a task that reachesbeyond the scope of this paper, although admittedly the notion of astrategys avoidance potential does provide a very natural basis forsuch quantifications.22

Finally, we note that the definition has both descriptive and nor-mative content. On the one hand we claim that any definition of

moral responsibility that connects outcomes to individuals will, oneway or another, take this form. That is, any ascription of this form ofresponsibility will refer to a game, the solution concepts (standards ofbehaviour), a causal condition, an eligibility function, and the

20 Goldmans solution is in fact a special case of Definition 5 in which he implicitly assigns

equi-probability to each possible strategy play.

21 Although we often make judgements of the form i bears more moral responsibility for x

than j, not everyone agrees that such statements are meaningful. See Zimmerman 1985 for an

argument against the notion that moral responsibility can be expressed in terms of relativeshares of a fixed sum.

22 In Braham and van Hees 2009 we demonstrate how such quantifications are possible for

purely causal contributions and therefore for conceptions of responsibility that are defined

purely in these terms. See also Felsenthal and Machover 2009.





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avoidance potential. On the other hand, the definition can be taken asnormative: any definition of moral responsibility ought to take thisform, that is to say, our constructive exercise demonstrates the proper

way to make such ascriptions.

7. Applications

With the machinery in place, our task now is to evaluate the threeexamples that we used to motivate our analysis in section 1. We focusfirst on the general collective action cases before turning to the moredifficult and subtle Frankfurt example. To keep the analysis tractable

we will avoid, as far as possible, the underlying formalisms that weoutlined in earlier sections, although this underlying formalism iswhat generates our answers.

7.1 The Tragedy of the CommonsThe Tragedy of the Commons (Hardin 1968) is a model that capturesa whole host of important collective action situations (global warm-ing, depletion of fish stocks, production of public goods, volunteer-

ing). In the narrative of the commons, and in collective actionproblems in general, no individual has direct control over the out-come in the form of actions that are necessary or sufficient conditionsfor such an outcome to occur. In such cases it is not obvious who isto be assigned responsibility for the outcome. To illustrate the highstakes involved, consider the issue of whether moral obligations re-garding global warming devolve upon individual people, given thatglobal warming can be traced back to countless day-to-day individualdecisions. As many have done, we can describe this situation as

a Tragedy of the Commons.23 In this case the commons is the climateand in one version suggested by Johnson (2003) and Sinnott-Armstrong (2005), the actions involved are, for instance, taking aspin in a gas-guzzling sport utility vehicle or not; the outcomes arethe many effects, including increased levels of carbon dioxide emis-sions, climate change, and eventual destruction of ecologically sensi-tive habitats. If we can pin responsibility on Sunday pleasure drivers,at least prima facie, an effective policy for the alleviation of global

warming should include educative measures that effect changes in theattitudes of the individuals involved. On the other hand, if, as both

23 This is the basic position of the now well-known Stern Review (Stern 2007). Other

problems of justice, such as world poverty, can also be modeled as a Tragedy of the Commons.





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Johnson and Sinnott-Armstrong believe, such drivers cannot be heldresponsible for global warning, then any such measures would beunjust in the sense that they place undeserved moral burdens on

individuals.To analyse in a particular case of the Tragedy of the Commons who

is responsible for the depletion of the commons, we could decide topresent the game corresponding to the case in detail, state the solutionconcept and corresponding probability functions, define the appro-priate eligibility mappings, and subsequently check whether our con-ditions for assigning responsibility are satisfied. However, we need notdo so. For our purposes it suffices to restrict ourselves to three general

characteristics that we assume all such situations to have in common.(i) The bad outcome could have been prevented, that is to say, thegame in question has at least one other outcome. (ii) Before the gamewas played, each agent assigned at least some positive probability tothe strategy combination the others actually did play. (iii) Regardlessof the strategies of the others, each individual had at least one eligiblestrategy by which he would not be effective for the outcome.

The alternative strategy by which an individual would not have beeneffective is usually taken to be some sort of restriction on the part of

the player, such as a restriction of the number of livestock a farmerbrings to the commons, a reduction of ones carbon footprint activ-ities, and so forth. Note that we assume that each individual has oneor more of such restricting strategies. The assumption is not innocu-ous and will not be satisfied in each tragedy of the commons: if notsending any of his livestock to the commons means that a farmer andhis family will starve to death for lack of income or food, then it is notreasonable to demand that he do so.

Given these characteristics, it is not only easy to see that some in-dividuals are responsible for the outcome but also that all individualswho causally contributed to the outcome are so. That at least some ofthe individuals are causally effective for the outcome follows from thefirst characteristic. That is, it entails that some subset of the strategiesactually played forms a minimal sufficient condition for the outcome.Now take any of the players whose strategy is a part of such a min-imally sufficient condition. The second characteristic states that theplayer had a (justified true) belief that he might be causally effective

for the outcome. Since, by the third characteristic, he could haveensured that he would not make a causal contribution, and sincedoing so would have been eligible, it follows that he is morallyresponsible.





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We infer that an excuse of the form given that I could reason-ably and correctly have expected each of the other agents toplay their polluting strategy I cannot be blamed for doing so too

because my contribution to the depletion of the resource would nothave any noticeable effect will not pass. In other words, a failure ofcollective action does not have a moral correlate in the form of afailure of individual responsibility, as Hardin (1988, pp. 1567) ap-pears to suggest. And thus in contrast to, say, Johnson (2003) andSinnott-Armstrong (2005), our framework will assign responsibilityfor global warming and its manifold effects from frivolous pollutingactivities.

7.2 The Discursive DilemmaOur next application concerns the recent argument put forward byPettit (2007) in which he claims that situations exist in which a col-lective is responsible for its actions, even though none of its membersare.24 He makes use of the so-called Discursive Dilemma to generatethis result. This is a situation in which members of a committee haveto make a decision about the enactment of a specific policy. In Pettits

example, the committee consists of co-workers who have to decidewhether they agree to a pay sacrifice in order to buy and install a workfloor safety device. Rather than putting that decision directly to a vote,the committee rules specify that the decision will be taken if, and onlyif, the committee comes to a positive verdict on three issues: whetherthere is a real danger, whether the safety device is effective, andwhether the pay sacrifice is bearable. Furthermore, the rules specifythat a vote will be taken on each of the three issues separately and thateach issue must be decided by majority vote. To simplify matters,

assume, as Pettit does, that the committee consists of three members.Table 1 describes their views on the three issues as well as whether thepay sacrifice is indeed justified.

Each individual is thus opposed to the pay sacrifice, but for differ-ent reasons: adoes not believe the salary cut is reasonable, bdoes notthink the device is effective, and c does not believe there is a real

24 We thus take what we call a responsibility void to be a situation in which none of the

individuals bear any responsibility for the outcome. In fairness to Pettit, it should be noted

that he leaves open the possibility that responsibility voids need not consist of such a completeshortfall in individual responsibility but may already exist if each of the committee members

bears only a very diminished level of personal responsibility for the outcome (p. 198). Since

we do not derive judgements about degrees of responsibility, our analysis of the Discursive

Dilemma does not say anything about such partial responsibility voids.





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